arbitrate

If your two best friends are fighting over the last piece of gum in the pack, you might arbitrate by telling them to split the last piece. Arbitrate is when a neutral third party helps end a conflict.

Arbitrate derives from the Latin arbiter "judge." (An arbiter of taste is a good judge of taste.) When you arbitrate, you are doing what a judge does in a court of law. In the US, to avoid litigation, many choose non-binding arbitration—where a neutral third party suggests a settlement.